Undersampled Critical Branching Processes on Small-World and Random Networks Fail to Reproduce the Statistics of Spike Avalanches

The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality in the brain. This evidence is supported by the fact that a critical branching process exhibits the same exponent t~3=2. Models at criticality have been employed to mimic avalanche propagation and explain the statistics observed experimentally. However, a crucial aspect of neuronal recordings has been almost completely neglected in the models: undersampling. While in a typical multielectrode array hundreds of neurons are recorded, in the same area of neuronal tissue tens of thousands of neurons can be found. Here we investigate the consequences of undersampling in models with three different topologies (two-dimensional, small-world and random network) and three different dynamical regimes (subcritical, critical and supercritical). We found that undersampling modifies avalanche size distributions, extinguishing the power laws observed in critical systems. Distributions from subcritical systems are also modified, but the shape of the undersampled distributions is more similar to that of a fully sampled system. Undersampled supercritical systems can recover the general characteristics of the fully sampled version, provided that enough neurons are measured. Undersampling in two-dimensional and small-world networks leads to similar effects, while the random network is insensitive to sampling density due to the lack of a well-defined neighborhood. We conjecture that neuronal avalanches recorded from local field potentials avoid undersampling effects due to the nature of this signal, but the same does not hold for spike avalanches. We conclude that undersampled branching-process-like models in these topologies fail to reproduce the statistics of spike avalanches.

Relações ecologicas entre caranguejos e composição arbórea em bosques de mangue naturais e restaurados no nordeste brasileiro

This study aimed to compare the development of crab and tree communities of two restored mangrove areas, one planted with Rhizophora mangle and the other naturally recovered, and also to compare the predation of Grapsid crab Goniopsis cruentata and the Ocypodid Ucides cordatus over the propagules of three mangrove trees: Rhizophora mangle, Avicennia schaueriana e Laguncularia racemosa. Specifically, we tested the hypothesis that Goniopsis predation is more important that Ucides predation, and that these consumers have antagonist effects over propagule consumption. In each area, 10 quadrates were selected at random to analyze tree richness, diameter, height, tree biomass and crab richness and density five years after restoration experiment start. Results show that tree height, biomass and crab density were significantly higher in artificially restored area. No significant differences were observed in crab species richness between areas, but higher tree richness was observed in self-recovered area. Results suggest that planting propagules of Rhizophora can significantly increase tree recovering if the aim was increase tree biomass and crab density, which can accelerate return of ecological functionality. Goniopsis is a more important propagule predator than Ucides both in natural and restored areas. The effects of Goniopis were higher in absence of Ucides, due to negative interactions among these two predator species. The preference of Goniopsis by Avicennia and Laguncularia can favor the dominance of Rhizophora observed in Neotropical mangroves. This study suggests that propagule predation by Goniopsis should be controlled in restoration programs, if dominance of Rhizophora is undesirable respect to more rich tree communities